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Phase Difference Calculator

Find phase difference between two coherent waves from path difference

Parameters

mⓘ
mⓘ
Show Trail

Controls

xⓘ

Calculated Values

Phase Difference:
1.57;rad1.57;rad
Phase (degrees):
90.00;°90.00;°

Examples

Destructive

Δx = λ/2.

    Constructive

    Δx = 2λ.

      Visualization

      Phase Difference and Path Difference in Interference

      Two coherent wave sources emit waves with a constant phase relationship (same frequency, stable phase). Where their crests align, they interfere constructively; where crest meets trough, destructively. The key variable is path difference Δx — extra distance one wave travels compared to the other.

      Phase difference Δφ (radians) relates to path difference by Δφ = 2πΔx/λ, where λ is wavelength in the medium. One full wavelength path difference = 2π rad phase shift = 360°. Divide by λ to count how many wavelengths “fit” in Δx.

      Constructive interference: Δx = mλ (m = 0, ±1, ±2, …) → Δφ = 2πm. Destructive: Δx = (m + ½)λ → Δφ = (2m+1)π. Partial interference between gives intermediate amplitude (use superposition formula).

      Young double-slit experiment: two slits separated by d give path difference Δx ≈ d sin θ at angle θ from center. Bright fringes when d sin θ = mλ; dark when d sin θ = (m+½)λ. Fringe spacing on screen distance L: β = λL/d.

      Reflection can add π phase (180°): wave reflecting from a denser medium (higher impedance) inverts; from rarer medium it may not. This shifts fringe patterns in thin films and affects standing waves on strings (fixed end ≈ node).

      Coherence requires same ω and stable φ; laser light is highly coherent; two independent light bulbs are not — no steady fringe pattern. Temporal coherence length matters for white light.

      Class 12 NCERT Interference and Diffraction. JEE combines Δφ with geometry (slits, thin films, Newton rings) and may ask convert radians ↔ degrees.

      Key Concepts

      • Δφ = 2πΔx/λ
      • Constructive: Δx = mλ
      • Destructive: Δx = (m + ½)λ
      • Young: Δx = d sin θ
      • Fringe spacing β = λL/d
      • Reflection π shift at denser medium

      Real-World Applications

      • Young double-slit and fringe measurement
      • Thin-film interference (soap, oil, coatings)
      • Microwave and ripple-tank interference labs
      • Optical interferometry (Michelson, LIGO concept)
      • Class 12–JEE path difference and fringe problems

      Explore Further

      More waves tools

      • Wave Properties

        Calculate wavelength, frequency, amplitude, and wave velocity.

      • Doppler Effect

        Analyze frequency shifts due to relative motion of source and observer.

      • Wave Interference

        Analyze constructive and destructive interference patterns between two waves with interactive visualization.

      • Standing Waves

        Analyze standing wave patterns, nodes, antinodes, and resonance frequencies.

      • Wave Reflection

        Calculate reflection coefficients, phase shifts, and energy transfer at boundaries.

      • Wave Transmission

        Analyze wave transmission between different media and wavelength changes.

      Physics Equations

      Phase Difference:
      Δϕ=2πΔxλ\Delta\phi = \frac{2\pi\Delta x}{\lambda}

      Step-by-Step Solution

      See how the main results are calculated.

      1

      Step 1: Phase from Path Difference

      Equation:

      Δϕ=2πΔxλ\Delta\phi = \frac{2\pi\Delta x}{\lambda}

      Explanation:

      Path difference Δx between two coherent sources or rays.

      2

      Step 2: Given

      Result:

      Δx=0.5m,λ=2mΔx = 0.5 m, λ = 2 m
      3

      Step 3: Calculate

      Calculation:

      Δϕ=2π×0.52=1.5708rad\Delta\phi = \frac{2\pi \times 0.5}{2} = 1.5708 rad

      Result:

      Δφ=1.5708rad(90.00°)Δφ = 1.5708 rad (90.00°)
      4

      Step 4: Constructive

      Δφ = 2πm (m integer) → constructive interference

      Explanation:

      Δx = mλ

      5

      Step 5: Destructive

      Δφ = (2m+1)π → destructive

      Explanation:

      Δx = (m + ½)λ

      6

      Step 6: Young's Slit Link

      Equation:

      Δx=dsin⁡θ\Delta x = d\sin\theta

      Explanation:

      Fringe spacing connects geometry to phase difference.

      Frequently Asked Questions (FAQ)

      Radians or degrees?

      Physics formulas use radians. Δφ(deg) = (180/π) × Δφ(rad). Calculator may use either — be consistent.

      What if Δx > many λ?

      Use fractional part: effective Δx mod λ determines interference type; integer multiples of λ are constructive.

      Does amplitude affect Δφ?

      No. Phase difference depends on geometry and λ, not on A₁, A₂ (for same ω).

      Phase vs path difference?

      Path difference is distance (m); phase difference is angle (rad). Linked by 2π/λ factor.

      White light fringes?

      Each λ has fringes at different positions — colored patterns; central white fringe where all constructively overlap.

      Practice MCQs

      1. Phase difference:
      2. Constructive:
      3. Destructive:
      4. Δφ = π means:
      5. Coherent sources need:
      6. Double slit path diff:

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